The former Atlanta Braves superstar appeared on 61.6 percent of the writers' ballots in the latest round of HOF voting last month ... up from 58.1 percent last year.

But, with players needing at least 75 percent in order to officially get a plaque in Cooperstown, he fell short for the seventh straight year.

However, when we spoke with the 10-time Gold Glover out at Super Bowl week in Las Vegas earlier this month ... he told us he wasn't sweating things one bit.

Obviously, he'd love to get in ... but he explained, "If I don't make it, I will be the same person."

Jones certainly has a deserving resume. In his 17 Big League seasons, he made five All-Star teams and smacked 434 home runs with a .254 batting average. He also tallied 1,933 hits and 1,289 RBIs.

"I'm gracious that I'm still on [the ballot]," said Jones, who has three years left of eligibility. "Hopefully I can say one day I make it."

Meanwhile, Jones' son, Druw Jones, is trying to begin building a Hall of Fame resume of his own sooner rather than later after the Arizona Diamondbacks took him with the No. 2 overall pick in the 2022 draft.

Andruw says he's hoping his boy has a better career than he had ... although he made sure to say he won't be bothered if the younger Jones never suits up for his beloved Braves.